This is basically an impossible battle.....
The Logia users of the Shichibukai are untouchable by any of the other two forces. At the same time, all of the Espada are living spirits so the other two groups can't even see them.
Akatsuki is basically screwed because of the Logia users..
So basically it comes down to can the Espada take the souls of the Logia users?! If so, then the Espada win...if not, a tie between the Espada and Shichibukai.
However, if we are going on a principle that everyone can see each other....then the Schichibukai simply because the Logia users are literally untouchable considering the other two groups can't use Haki...